QREigenComponentExtractor.java

  1. package org.drip.numerical.eigen;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  14.  * 
  15.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  16.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  17.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  18.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  19.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  20.  *      and computational support.
  21.  *  
  22.  *      https://lakshmidrip.github.io/DROP/
  23.  *  
  24.  *  DROP is composed of three modules:
  25.  *  
  26.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  27.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  28.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  29.  * 
  30.  *  DROP Product Core implements libraries for the following:
  31.  *  - Fixed Income Analytics
  32.  *  - Loan Analytics
  33.  *  - Transaction Cost Analytics
  34.  * 
  35.  *  DROP Portfolio Core implements libraries for the following:
  36.  *  - Asset Allocation Analytics
  37.  *  - Asset Liability Management Analytics
  38.  *  - Capital Estimation Analytics
  39.  *  - Exposure Analytics
  40.  *  - Margin Analytics
  41.  *  - XVA Analytics
  42.  * 
  43.  *  DROP Computational Core implements libraries for the following:
  44.  *  - Algorithm Support
  45.  *  - Computation Support
  46.  *  - Function Analysis
  47.  *  - Model Validation
  48.  *  - Numerical Analysis
  49.  *  - Numerical Optimizer
  50.  *  - Spline Builder
  51.  *  - Statistical Learning
  52.  * 
  53.  *  Documentation for DROP is Spread Over:
  54.  * 
  55.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  56.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  57.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  58.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  59.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  60.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  61.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  62.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  63.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  64.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  65.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  66.  * 
  67.  *  Licensed under the Apache License, Version 2.0 (the "License");
  68.  *      you may not use this file except in compliance with the License.
  69.  *   
  70.  *  You may obtain a copy of the License at
  71.  *      http://www.apache.org/licenses/LICENSE-2.0
  72.  *  
  73.  *  Unless required by applicable law or agreed to in writing, software
  74.  *      distributed under the License is distributed on an "AS IS" BASIS,
  75.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  76.  *  
  77.  *  See the License for the specific language governing permissions and
  78.  *      limitations under the License.
  79.  */

  81. /**
  82.  * <i>QREigenComponentExtractor</i> extracts the Eigenvalues and Eigenvectors using QR Decomposition.
  83.  * 
  84.  * <br><br>
  85.  *  <ul>
  86.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  87.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  88.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical">Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities</a></li>
  89.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/numerical/eigen">QR PICE Eigen-Component Extraction Methodologies</a></li>
  90.  *  </ul>
  91.  * <br><br>
  92.  *
  93.  * @author Lakshmi Krishnamurthy
  94.  */

  96. public class QREigenComponentExtractor
  97.     implements org.drip.numerical.eigen.ComponentExtractor
  98. {
  99.     private int _maxIterations = -1;
  100.     private double _tolerance = java.lang.Double.NaN;

  102.     /**
  103.      * QREigenComponentExtractor Constructor
  104.      * 
  105.      * @param maxIterations Maximum Number of Iterations
  106.      * @param tolerance Tolerance
  107.      * 
  108.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  109.      */

  111.     public QREigenComponentExtractor (
  112.         final int maxIterations,
  113.         final double tolerance)
  114.         throws java.lang.Exception
  115.     {
  116.         if (0 >= (_maxIterations = maxIterations) ||
  117.             !org.drip.numerical.common.NumberUtil.IsValid (
  118.                 _tolerance = tolerance
  119.             ) || 0. == _tolerance
  120.         )
  121.         {
  122.             throw new java.lang.Exception ("QREigenComponentExtractor ctr: Invalid Inputs!");
  123.         }
  124.     }

  126.     /**
  127.      * Retrieve the Maximum Number of Iterations
  128.      * 
  129.      * @return The Maximum Number of Iterations
  130.      */

  132.     public int maxIterations()
  133.     {
  134.         return _maxIterations;
  135.     }

  137.     /**
  138.      * Retrieve the Tolerance Level
  139.      * 
  140.      * @return The Tolerance Level
  141.      */

  143.     public double tolerance()
  144.     {
  145.         return _tolerance;
  146.     }

  148.     @Override public org.drip.numerical.eigen.EigenOutput eigenize (
  149.         final double[][] a)
  150.     {
  151.         org.drip.numerical.linearalgebra.QR qr = org.drip.numerical.linearalgebra.Matrix.QRDecomposition (
  152.             a
  153.         );

  155.         if (null == qr)
  156.         {
  157.             return null;
  158.         }

  160.         double[][] q = qr.q();

  162.         double[][] qTranspose = org.drip.numerical.linearalgebra.Matrix.Transpose (
  163.             q
  164.         );

  166.         if (null == qTranspose)
  167.         {
  168.             return null;
  169.         }

  171.         int iterationIndex = 0;
  172.         int eigenComponentCount = a.length;
  173.         double[] eigenvalueArray = new double[eigenComponentCount];
  174.         double[][] b = new double[eigenComponentCount][eigenComponentCount];
  175.         double[][] v = new double[eigenComponentCount][eigenComponentCount];

  177.         if (0 == eigenComponentCount || null == qTranspose[0] || eigenComponentCount != qTranspose[0].length)
  178.         {
  179.             return null;
  180.         }

  182.         for (int rowIndex = 0;
  183.             rowIndex < eigenComponentCount;
  184.             ++rowIndex)
  185.         {
  186.             for (int columnIndex = 0;
  187.                 columnIndex < eigenComponentCount;
  188.                 ++columnIndex)
  189.             {
  190.                 b[rowIndex][columnIndex] = q[rowIndex][columnIndex];
  191.                 v[rowIndex][columnIndex] = a[rowIndex][columnIndex];
  192.             }
  193.         }

  195.         while (iterationIndex++ < _maxIterations &&
  196.             org.drip.numerical.linearalgebra.Matrix.NON_TRIANGULAR ==
  197.             org.drip.numerical.linearalgebra.Matrix.TriangularType (
  198.                 v,
  199.                 _tolerance
  200.             )
  201.         )
  202.         {
  203.             if (null == (qr = org.drip.numerical.linearalgebra.Matrix.QRDecomposition (
  204.                 v = org.drip.numerical.linearalgebra.Matrix.Product (
  205.                     qTranspose,
  206.                     org.drip.numerical.linearalgebra.Matrix.Product (
  207.                         v,
  208.                         q
  209.                     )
  210.                 )
  211.             )))
  212.             {
  213.                 return null;
  214.             }

  216.             qTranspose = org.drip.numerical.linearalgebra.Matrix.Transpose (
  217.                 q = qr.q()
  218.             );

  220.             b = org.drip.numerical.linearalgebra.Matrix.Product (
  221.                 b,
  222.                 q
  223.             );
  224.         }

  226.         if (iterationIndex >= _maxIterations)
  227.         {
  228.             return null;
  229.         }

  231.         for (int rowIndex = 0;
  232.             rowIndex < eigenComponentCount;
  233.             ++rowIndex)
  234.         {
  235.             eigenvalueArray[rowIndex] = v[rowIndex][rowIndex];
  236.         }

  238.         try
  239.         {
  240.             return new org.drip.numerical.eigen.EigenOutput (
  241.                 org.drip.numerical.linearalgebra.Matrix.Transpose (
  242.                     b
  243.                 ),
  244.                 eigenvalueArray
  245.             );
  246.         } catch (java.lang.Exception e)
  247.         {
  248.             e.printStackTrace();
  249.         }

  251.         return null;
  252.     }

  254.     /**
  255.      * Generate the Ordered List of Eigenvalues for the specified Eigen-output
  256.      * 
  257.      * @param eigenOutput The Eigen Output
  258.      * 
  259.      * @return The Order List
  260.      */

  262.     public java.util.List<java.lang.Integer> eigenComponentOrderList ( 
  263.         final org.drip.numerical.eigen.EigenOutput eigenOutput)
  264.     {
  265.         if (null == eigenOutput)
  266.         {
  267.             return null;
  268.         }

  270.         double[] eigenvalueArray = eigenOutput.eigenValueArray();

  272.         int eigenComponentCount = eigenvalueArray.length;

  274.         java.util.List<java.lang.Double> eigenValueList = new java.util.ArrayList<java.lang.Double>();

  276.         java.util.List<java.lang.Integer> eigenValueOrder = new java.util.ArrayList<java.lang.Integer>();

  278.         for (int eigenComponentIndex = 0;
  279.             eigenComponentIndex < eigenComponentCount;
  280.             ++eigenComponentIndex)
  281.         {
  282.             int eigenValueOrderSize = eigenValueOrder.size();

  284.             if (0 == eigenValueOrderSize)
  285.             {
  286.                 eigenValueOrder.add (
  287.                     eigenComponentIndex
  288.                 );

  290.                 eigenValueList.add (
  291.                     eigenvalueArray[eigenComponentIndex]
  292.                 );
  293.             }
  294.             else
  295.             {
  296.                 int insertionIndex = 0;

  298.                 for (int eigenValueOrderIndex = 0;
  299.                     eigenValueOrderIndex < eigenValueOrderSize;
  300.                     ++eigenValueOrderIndex)
  301.                 {
  302.                     if (eigenvalueArray[eigenComponentIndex] <= eigenValueList.get (
  303.                         eigenValueOrderIndex
  304.                     ))
  305.                     {
  306.                         insertionIndex = eigenValueOrderIndex;
  307.                         break;
  308.                     }
  309.                 }

  311.                 eigenValueOrder.add (
  312.                     insertionIndex,
  313.                     eigenComponentIndex
  314.                 );

  316.                 eigenValueList.add (
  317.                     insertionIndex,
  318.                     eigenvalueArray[eigenComponentIndex]
  319.                 );
  320.             }
  321.         }

  323.         return eigenValueOrder;
  324.     }

  326.     /**
  327.      * Generate the Ordered List of Eigen Components arranged by Ascending Eigenvalue
  328.      * 
  329.      * @param a Input Matrix
  330.      * 
  331.      * @return The Ordered List of Eigen Components arranged by Ascending Eigenvalue
  332.      */

  334.     public org.drip.numerical.eigen.EigenComponent[] orderedEigenComponentArray (
  335.         final double[][] a)
  336.     {
  337.         org.drip.numerical.eigen.EigenOutput eigenOutput = eigenize (
  338.             a
  339.         );

  341.         java.util.List<java.lang.Integer> eigenComponentOrderList = eigenComponentOrderList (
  342.             eigenOutput
  343.         );

  345.         if (null == eigenComponentOrderList)
  346.         {
  347.             return null;
  348.         }

  350.         double[] eigenValueArray = eigenOutput.eigenValueArray();

  352.         double[][] eigenVectorArray = eigenOutput.eigenVectorArray();

  354.         int eigenComponentCount = eigenComponentOrderList.size();

  356.         org.drip.numerical.eigen.EigenComponent[] eigenComponentArray =
  357.             new org.drip.numerical.eigen.EigenComponent[eigenComponentCount];

  359.         for (int eigenComponentIndex = 0;
  360.             eigenComponentIndex < eigenComponentCount;
  361.             ++eigenComponentIndex)
  362.         {
  363.             int eigenComponentOrder = eigenComponentOrderList.get (
  364.                 eigenComponentIndex
  365.             );

  367.             try
  368.             {
  369.                 eigenComponentArray[eigenComponentIndex] = new org.drip.numerical.eigen.EigenComponent (
  370.                     eigenVectorArray[eigenComponentOrder],
  371.                     eigenValueArray[eigenComponentOrder]
  372.                 );
  373.             }
  374.             catch (java.lang.Exception e)
  375.             {
  376.                 e.printStackTrace();

  378.                 return null;
  379.             }
  380.         }

  382.         return eigenComponentArray;
  383.     }

  385.     @Override public org.drip.numerical.eigen.EigenComponent principalComponent (
  386.         final double[][] a)
  387.     {
  388.         org.drip.numerical.eigen.EigenComponent[] eigenComponentArray = orderedEigenComponentArray (
  389.             a
  390.         );

  392.         return null == eigenComponentArray ? null : eigenComponentArray[0];
  393.     }

  395.     /**
  396.      * Generate the UD Form of the Input Matrix
  397.      * 
  398.      * @param a The Input Matrix
  399.      * 
  400.      * @return The UD Form
  401.      */

  403.     public org.drip.numerical.linearalgebra.UD udForm (
  404.         final double[][] a)
  405.     {
  406.         org.drip.numerical.eigen.EigenComponent[] eigenComponentArray = orderedEigenComponentArray (
  407.             a
  408.         );

  410.         if (null == eigenComponentArray)
  411.         {
  412.             return null;
  413.         }

  415.         int eigenComponentCount = eigenComponentArray.length;
  416.         double[][] d = new double[eigenComponentCount][eigenComponentCount];
  417.         double[][] u = new double[eigenComponentCount][];

  419.         for (int eigenComponentIndexI = 0;
  420.             eigenComponentIndexI < eigenComponentCount;
  421.             ++eigenComponentIndexI)
  422.         {
  423.             u[eigenComponentIndexI] = eigenComponentArray[eigenComponentIndexI].eigenVector();

  425.             for (int eigenComponentIndexJ = 0;
  426.                 eigenComponentIndexJ < eigenComponentCount;
  427.                 ++eigenComponentIndexJ)
  428.             {
  429.                 d[eigenComponentIndexI][eigenComponentIndexJ] = eigenComponentIndexI != eigenComponentIndexJ
  430.                     ? 0. : eigenComponentArray[eigenComponentIndexI].eigenValue();
  431.             }
  432.         }

  434.         try
  435.         {
  436.             return new org.drip.numerical.linearalgebra.UD (
  437.                 u,
  438.                 d
  439.             );
  440.         }
  441.         catch (java.lang.Exception e)
  442.         {
  443.             e.printStackTrace();
  444.         }

  446.         return null;
  447.     }
  448. }
Created with JaCoCo 0.7.9.201702052155